Pendulum as Vibration Absorber for Flexible Structures: Experiments and Theory

The dynamic response ofa beam-tip mass-pendulum system subjected to a sinusoidal excitation is investigated. A simple pendulum mounted to a tip mass of a beam is used as a vibration absorber. The nonlinear equations of motion are developed to investigate the autoparametric interaction between the first two modes of the system. The nonlinear terms appear due to the curvature of the beam and the coupling effect between the beam and pendulum. Complete energy transfer between modes is shown to occur when the beam frequency is twice the pendulum frequency. Experimental results are compared with a theoretical solution obtained using numerical integration. The experimental results are in qualitative agreement with the theory.

[1]  A. D. S. Barr,et al.  The Autoparametric Vibration Absorber , 1972 .

[2]  Sami F. Masri,et al.  Theory of the Dynamic Vibration Neutralizer With Motion-Limiting Stops , 1972 .

[3]  Sami F. Masri,et al.  On the stability of the impact damper. , 1966 .

[4]  J. Hunt,et al.  The broadband dynamic vibration absorber , 1982 .

[5]  H. Hatwal,et al.  Notes on an Autoparametric Vibration Absorber , 1982 .

[6]  J. H. Heinbockel,et al.  Resonant Oscillations of a Beam-Pendulum System , 1963 .

[7]  B. Schmalhorst,et al.  Optimization of a non-linear dynamic vibration absorber , 1985 .

[8]  Stephen Gates,et al.  Transverse vibration and buckling of a cantilevered beam with tip body under axial acceleration , 1985 .

[9]  R. A. Ibrahim,et al.  Parametric Vibration Part IV: Current Problems (2) , 1978 .

[10]  H. Hatwal,et al.  Forced Nonlinear Oscillations of an Autoparametric System—Part 1: Periodic Responses , 1983 .

[11]  A. H. Nayfeh,et al.  The Non-Linear Response of a Slender Beam Carrying a Lumped Mass to a Principal Parametric Excitation: Theory and Experiment , 1989 .

[12]  Hideo Saito,et al.  The Parametric Response of a Horizontal Beam Carrying a Concentrated Mass Under Gravity , 1978 .

[13]  Hiroyuki Kojima,et al.  Nonlinear Vibrations of a Beam with a Mass Subjected to Alternating Electromagnetic Force , 1985 .

[14]  J. Shaw,et al.  The Onset of Chaos in a Two-Degree-of-Freedom Impacting System , 1989 .

[15]  W. H. Liu,et al.  Vibrations of a constrained beam carrying a heavy tip body , 1988 .

[16]  Raouf A. Ibrahim,et al.  AUTOPARAMETRIC RESONANCE IN A STRUCTURE CONTAINING A LIQUID, PART I: TWO MODE INTERACTION , 1975 .

[17]  A. Ertas,et al.  Real-time response of the simple pendulum: An experimental technique , 1992 .

[18]  Wanda Szemplińska-Stupnicka.  On the phenomenon of the combination type resonance in non-linear two-degree-of-freedom systems , 1969 .

[19]  M. Gürgöze,et al.  On the approximate determination of the fundamental frequency of a restrained cantilever beam carrying a tip heavy body , 1986 .

[20]  P.A.A. Laura,et al.  A note on the vibrations of a clamped-free beam with a mass at the free end , 1974 .

[21]  A. Ertas,et al.  Non-linear dynamic response of a rotating machine , 1990 .

[22]  Dean T. Mook,et al.  Theoretical and experimental study of modal interaction in a two-degree-of-freedom structure , 1984 .

[23]  Eugene Sevin,et al.  On the Parametric Excitation of Pendulum-Type Vibration Absorber , 1961 .